Entropic fluctuations in XY chains and reflectionless Jacobi matrices

We study the entropic fluctuations of a general XY spin chain where initially the left(x0) part of the chain is in thermal equilibrium at inverse temperature Tl/Tr. The temperature differential results in a non-trivial energy/entropy flux across the chain. The Evans-Searles (ES) entropic functional describes fluctuations of the flux observable with respect to the initial state while the Gallavotti-Cohen (GC) functional describes these fluctuations with respect to the steady state (NESS) the chain reaches in the large time limit. We also consider the full counting statistics (FCS) of the energy/entropy flux associated to a repeated measurement protocol, the variational entropic functional (VAR) that arises as the quantization of the variational characterization of the classical Evans-Searles functional and a natural class of entropic functionals that interpolate between FCS and VAR. We compute these functionals in closed form in terms of the scattering data of the Jacobi matrix h canonically associated to the XY chain. We show that all these functionals are identical if and only if h is reflectionless (we call this phenomenon entropic identity). If h is not reflectionless, then the ES and GC functionals remain equal but differ from the FCS, VAR and interpolating functionals. Furthermore, in the non-reflectionless case, the ES/GC functional does not vanish at 1 (i.e., the Kawasaki identity fails) and does not have the celebrated ES/GC symmetry. The FCS, VAR and interpolating functionals always have this symmetry. In the cases where h is a Schr\"odinger operator, the entropic identity leads to some unexpected open problems in the spectral theory of one-dimensional discrete Schr\"odinger operators

A compact design for the Josephson mixer: the lumped element circuit

We present a compact and efficient design in terms of gain, bandwidth and dynamical range for the Josephson mixer, the superconducting circuit performing three-wave mixing at microwave frequencies. In an all lumped-element based circuit with galvanically coupled ports, we demonstrate non degenerate amplification for microwave signals over a bandwidth up to 50 MHz for a power gain of 20 dB. The quantum efficiency of the mixer is shown to be about 70$\%$ and its saturation power reaches $-112$ dBm.Comment: 5 pages, 4 figure

Optimized production of large Bose Einstein Condensates

We suggest different simple schemes to efficiently load and evaporate a ''dimple'' crossed dipolar trap. The collisional processes between atoms which are trapped in a reservoir load in a non adiabatic way the dimple. The reservoir trap can be provided either by a dark SPOT Magneto Optical Trap, the (aberrated) laser beam itself or by a quadrupolar or quadratic magnetic trap. Optimal parameters for the dimple are derived from thermodynamical equations and from loading time, including possible inelastic and Majorana losses. We suggest to load at relatively high temperature a tight optical trap. Simple evaporative cooling equations, taking into account gravity, the possible occurrence of hydrodynamical regime, Feshbach resonance processes and three body recombination events are given. To have an efficient evaporation the elastic collisional rate (in s$^{-1}$) is found to be on the order of the trapping frequency and lower than one hundred times the temperature in micro-Kelvin. Bose Einstein condensates with more than $10^7$ atoms should be obtained in much less than one second starting from an usual MOT setup.Comment: 14 page

A note on the Landauer principle in quantum statistical mechanics

The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than $kTlog 2$. We discuss Landauer's principle for quantum statistical models describing a finite level quantum system S coupled to an infinitely extended thermal reservoir R. Using Araki's perturbation theory of KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural ergodicity assumption on the joint system S+R, that Landauer's bound saturates for adiabatically switched interactions. The recent work of Reeb and Wolf on the subject is discussed and compared

Three dimensional structure of penumbral filaments from Hinode observations

We analyse spectropolarimetric observations of the penumbra of the NOAA AR 10953 at high spatial resolution (0.3"). The full Stokes profiles of the Fe I lines at 630.1 nm and 630.2 nm have been obtained with the Solar Optical Telescope (SOT) on board the Hinode satellite. The data have been inverted by means of the SIR code, deriving the stratifications of temperature, line of sight velocity, and the components of the magnetic field vector in optical depth. In order to evaluate the gas pressure and to obtain an adequate geometrical height scale, the motion equation has been integrated for each pixel taking into account the terms of the Lorentz force. To establish the boundary condition, a genetic algorithm has been applied. The final resulting magnetic field has a divergence compatible with 0 inside its uncertainties. First analyses of the correlation of the Wilson depression with velocity, temperature, magnetic field strength, and field inclination strongly support the uncombed penumbral model proposed by Solanki & Montavon (1993).Comment: 6 pages, 3 figures, conference proceeding: SEA meeting 2008, Santander, Spai

Copilot Pro®: A full method for a steering of the machining.

International audienceCopilot Pro® is a method for the initial and regular machine-tools setup, developed by the Symme laboratory of the Savoy University and by the Technical Center of Industries of Screw-machining (Ctdec) in France. Its first step is the organization of the different machining operations, in setup steps, themselves subdivided into measuring steps. The second step consists in determining the manufacturing dimensions to measure at the end of each measuring step. Finally, the third step consists in linking the manufacturing dimensions to both the correctors and the tool-dimensions, in the aim of calculating the corrections that have to be done in function of the deviations measured on the manufacturing dimensions. With this method, the steering of an industrial workpiece is performed with two steering parts instead of ten before

Supersonic Evershed flow outside Sunspots

We report on the discovery of mostly horizontal field channels just outside sunspot penumbrae (in the so-called `moat' region) that are seen to sustain supersonic flows (line-of-sight component of 6 km s{-1}). The spectral signature of these supersonic flows corresponds to circular polarization profiles with an additional, satellite, third lobe of the same sign as the parent sunspot' Stokes V blue lobe, for both downflows and upflows. This is consistent with an outward directed flow that we interpret as the continuation of the magnetized Evershed flow outside sunspots at supersonic speeds. In Stokes Q and U, a clear signature of a transverse field connecting the two flow streams is observed. Such an easily detectable spectral signature should allow for a clear identification of these horizontal field channels in other spectropolarimetric sunspot data. For the spot analyzed in this paper, a total of 5 channels with this spectral signature have been unambiguously found

Cooper pair sizes in 11Li and in superfluid nuclei: a puzzle?

We point out a strong influence of the pairing force on the size of the two neutron Cooper pair in $^{11}$Li, and to a lesser extent also in $^6$He. It seems that these are quite unique situations, since Cooper pair sizes of stable superfluid nuclei are very little influenced by the intensity of pairing, as recently reported. We explore the difference between $^{11}$Li and heavier superfulid nuclei, and discuss reasons for the exceptional situation in $^{11}$Li.Comment: 9 pages. To be published in J. of Phys. G special issue on Open Problems in Nuclear Structure (OPeNST